Error Correction Codes (ECC) are used in a variety of applications, such as in various digital communication and data storage applications. Some systems use a special class of block codes called Low Density Parity Check (LDPC) codes. LDPC codes are described, for example, by Gallager, in “Low Density Parity Check Codes,” MIT Press, 1963, which is incorporated herein by reference. Chapter 4 of this book describes decoding of LDPC codes. Lin and Costello describe iterative algorithms for decoding LDPC codes, as well as several example decoder configurations, in “Error Control Coding,” Prentice Hall, second edition, June, 2004, Chapter 17.6, pages 871-880, which is incorporated herein by reference. Other example techniques for encoding and decoding of LDPC codes are described in U.S. Patent Application Publications 2009/0070659 and 2009/0249159, whose disclosures are incorporated herein by reference.
In some applications, a rate-compatible code is derived from a mother code using shortening, puncturing and/or extension of the mother code. Example techniques for designing, encoding and decoding Rate-compatible LDPC codes are described by Ha et al., in “Rate-Compatible Punctured Low Density Parity Check Codes with Short Block Lengths,” IEEE Transactions on Information Theory, volume 52, number 2, February, 2006, pages 728-738; by Li and Narayanan, in “Rate-Compatible Low Density Parity Check Codes for Capacity-Approaching ARQ Schemes in Packet Data Communication,” Proceedings of the International Conference on Communications, Internet and Information Technology (CIIT), U.S. Virgin Islands, November, 2002; and by Yazdani and Banihashemi, in “On Construction of Rate-Compatible Low-Density Parity-Check Codes,” Proceedings of the IEEE International Conference on Communication (ICC), Paris, France, June, 2004, pages 430-434, which are incorporated herein by reference.
Other example techniques for designing rate-compatible LDPC codes are described by Kim et al., in “Design of Rate-Compatible Irregular LDPC Codes for Incremental Redundancy Hybrid ARQ Schemes,” IEEE International Symposium on Information Theory (ISIT), Seattle, Wash., July, 2006, pages 1139-1143; by Kou et al., in “Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and New Results,” IEEE Transactions on Information Theory, volume 47, number 7, November, 2001, pages 2711-2736, which is incorporated herein by reference.
Rate-compatible codes are also addressed in IEEE standard 802.11n—2009, entitled “IEEE Standard for Information Technology—Telecommunications and Information Exchange Between Systems—Local and Metropolitan Area Networks—Specific Requirements Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications,” Oct. 29, 2009; and by Blahut, in “Algebraic Codes for Data Transmission,” Cambridge University Press, 2004, chapter 3, pages 62-63, which are incorporated herein by reference.